TY - JOUR

T1 - A hierarchical loss and its problems when classifying non-hierarchically

AU - Wu, Cinna

AU - Tygert, Mark

AU - LeCun, Yann

N1 - Publisher Copyright:
© 2019 Wu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - Failing to distinguish between a sheepdog and a skyscraper should be worse and penalized more than failing to distinguish between a sheepdog and a poodle; after all, sheepdogs and poodles are both breeds of dogs. However, existing metrics of failure (so-called "loss" or "win") used in textual or visual classification/recognition via neural networks seldom leverage a-priori information, such as a sheepdog being more similar to a poodle than to a skyscraper. We define a metric that, inter alia, can penalize failure to distinguish between a sheepdog and a skyscraper more than failure to distinguish between a sheepdog and a poodle. Unlike previously employed possibilities, this metric is based on an ultrametric tree associated with any given tree organization into a semantically meaningful hierarchy of a classifier's classes. An ultrametric tree is a tree with a so-called ultrametric distance metric such that all leaves are at the same distance from the root. Unfortunately, extensive numerical experiments indicate that the standard practice of training neural networks via stochastic gradient descent with random starting points often drives down the hierarchical loss nearly as much when minimizing the standard cross-entropy loss as when trying to minimize the hierarchical loss directly.

AB - Failing to distinguish between a sheepdog and a skyscraper should be worse and penalized more than failing to distinguish between a sheepdog and a poodle; after all, sheepdogs and poodles are both breeds of dogs. However, existing metrics of failure (so-called "loss" or "win") used in textual or visual classification/recognition via neural networks seldom leverage a-priori information, such as a sheepdog being more similar to a poodle than to a skyscraper. We define a metric that, inter alia, can penalize failure to distinguish between a sheepdog and a skyscraper more than failure to distinguish between a sheepdog and a poodle. Unlike previously employed possibilities, this metric is based on an ultrametric tree associated with any given tree organization into a semantically meaningful hierarchy of a classifier's classes. An ultrametric tree is a tree with a so-called ultrametric distance metric such that all leaves are at the same distance from the root. Unfortunately, extensive numerical experiments indicate that the standard practice of training neural networks via stochastic gradient descent with random starting points often drives down the hierarchical loss nearly as much when minimizing the standard cross-entropy loss as when trying to minimize the hierarchical loss directly.

UR - http://www.scopus.com/inward/record.url?scp=85076945310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076945310&partnerID=8YFLogxK

U2 - 10.1371/journal.pone.0226222

DO - 10.1371/journal.pone.0226222

M3 - Article

C2 - 31856228

AN - SCOPUS:85076945310

SN - 1932-6203

VL - 14

JO - PloS one

JF - PloS one

IS - 12

M1 - e0226222

ER -